A bookstore stocks 1/5 of its books as fiction works, and 1/3 less than the fiction books as self-help books. What fraction of the total books are fiction and self-help books?
A. 3/5
B. 11/30
C. 4/15
D. 2/15
E. 1/3
Answer: E
Source: Princeton Review
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A bookstore stocks 1/5 of its books as fiction works, and 1/3 less than the fiction books as self-help books. What fract
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A bookstore stocks 1/5 of its books as fiction works, and 1/3 less than the fiction books as self-help books. What fraction of the total books are fiction and self-help books?
Let the total number of books be B
A bookstore stocks 1/5 of its books as fiction works---> fiction work books = B/5
1/3 less than the fiction books ---> B/5 - B/5 * 1/3 = 2B/15 = SELF-HELP BOOKS
fiction and self-help books = B/5 + 2B/15 = 5B/15 = B/3
Now,
(fiction and self-help books)/total books = (B/3)/B = 1/3
Option E is the answer.
Let the total number of books be B
A bookstore stocks 1/5 of its books as fiction works---> fiction work books = B/5
1/3 less than the fiction books ---> B/5 - B/5 * 1/3 = 2B/15 = SELF-HELP BOOKS
fiction and self-help books = B/5 + 2B/15 = 5B/15 = B/3
Now,
(fiction and self-help books)/total books = (B/3)/B = 1/3
Option E is the answer.
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Solution:
We can let n = the total number of books and create the equations:
n/5 = fiction
and
n/5 x 2/3 = 2n/15 = self-help
Thus, fiction and self-help books are n/5 + 2n/15 = 3n/15 + 2n/15 = 5n/15 = n/3.
Answer: E
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